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Collateral Valuation In Clearing And Settlement System Narumon Saardchom* One of risk management techniques for clearing and settlement system is collateral requirement. The additional market risk from potential movement in collateral value between the time of pledging and liquidating could be captured and managed by haircut system. In this paper, haircut valuation models and framework are proposed and applied to different securities classes available in Thai market. Haircut rates are calculated based on both Value-at-Risk with normal distribution and with extreme value theory. Then, the accuracies of haircut are tested using BIS Basel back-testing framework. Finally, the optimal haircut rates are chosen based on risk-cost frontier analysis. JEL classification: C50, G28,G32 1. Introduction Settlement risk in securities trading and derivatives markets is managed under clearing and settlement system, in which risk modeling is a critical tool for measuring an appropriate collateral arrangement. The collateral most commonly used are instruments with low credit and liquidity risk. While larger amount of collateral provides higher security for clearing and settlement system, too large required collateral may discourage trading activities and inhibit the growth of capital markets. Therefore, an efficient risk management scheme for settlement system should be the one that balances between the counterparty risk and transaction costs for market participants. The amount of required collateral can be calculated by several methodologies, which lead to different results. Thus, the settlement risk for clearing and settlement system depend largely on the accuracy of collateral volatility valuation. In addition, there is a time lag between the time that the collateral is pledged and the time of potential default, at which point the value of collateral may decline. To prevent such additional risk, most exchanges adopt the haircut mechanism. Haircut represents the discounted value of collateral having to be pledged to take into account potential change in collateral value in the future. As a result, the higher the haircut rate, the larger collateral amount that must be pledged. Under BIS Basel II Capital Accord, banks are allowed to use a Value-at-Risk (VaR) measure to reflect the price volatility of the exposure and collateral. The Bank of * Dr Narumon Saardchom, Finance Department, NIDA Business School, Bangkok, Thailand Email: [email protected] Thailand also adopted VaR as a measure for haircuts used in banking regulation. In addition, the SEC’s system of haircuts in the US is a one-month 95% Value-at-Risk measure. VaR can be calculated by either parametric or non-parametric approach. The nonparametric approach does not make any assumption about the shape of the loss random variable. The nature of asymmetric loss distribution can be well taken care of with this approach, but VaR figure could be sensitive to information available in selected window period. The parametric approach relies on the assumption that the loss random variable belongs to a parametric family. Usually, asset returns are assumed to belong to a normal distribution. It is worth noting that there are some weaknesses of VaR; (i) VaR is measured with some errors from sampling variation and different statistical methodologies, (ii) VaR cannot describe the worst loss, and (iii) VaR cannot describe the loss in the left tail of the distribution. Although traditional practice and regulation are in favor of VaR for haircut valuation, VaR cannot fully capture market risk in extreme loss event, which is important for clearing and settlement system because default risk is likely to be high during an extreme event. That is, the counterparty is likely to default when the asset price largely declines. Garcia and Gencay (2006) propose an alternative approach for haircut valuation based on a VaR measure with a distribution based on extreme value theory that can better capture extreme tail loss. In this paper, we use the Thai data to calculate and compare haircut valuation based on a VaR with normality assumption and VaR with extreme value theory. The main objective is to derive the framework for calculating the most accurate haircut rate given available data. Then, haircut results are tested by BIS Basel back-testing. Finally, we adopt the risk-cost frontier analysis proposed by Garcia and Gencay (2006) to derive the optimal haircut rates. 2. Haircut Valuation Models The accuracy of haircut valuation is crucial for clearing and settlement system. Haircut should accurately capture volatility of security price that could be measured from the distribution of securities’ return. Thus, the accuracy of haircut valuation depends largely on the choice of probability distribution. Both SEC and Basel II capital accord recommend the use of VaR measure for haircut valuation because it could provide one figure representing the maximum price volatility with a given probability over a given time horizon. 2.1. VaR With Normality Assumption There are two main approaches for VaR calculation—parametric and non-parametric models. A non-parametric model makes no assumption on the distribution of securities’ return, but derive the distribution based on historical return data. The VaR result of a non-parametric model may fail to capture the extreme loss that is not included in the chosen data sample. Moreover, a VaR measure becomes more uncertain at higher confidence level. In contrast, a parametric model assumes that the securities’ return follow a parametric family such as a normal distribution. The VaR measure under a parametric approach is calculated by a following equation. VaR Z Where 1- is a confidence level, is expected securities’ return, is volatility of securities return, and z() is quantile of standard normal cumulative probability. Most clearinghouses rely on a parametric approach for haircut valuation based on VaR by assuming that securities return has a normal distribution. The disadvantage of this approach is that the VaR result will no longer be accurate when securities’ return does not have a normal distribution. Moreover, a VaR measure cannot capture extreme loss events, which is very important for clearing and settlement system because counterparty risk is likely to be high when the security prices drop significantly or when the securities’ returns are from the fat tail distribution. In such condition, haircut measure from VaR under normality assumption can be a critical source of error. 2.2. VaR With Extreme Value Theory McNeil (1999) and Garcia and Gencay (2006) propose an alternative approach, a VaR measure with the return distribution based on Extreme Value Theory (EVT) method, for haircut valuation of a fat tail return distribution. Since we are interested in the distribution of securities’ return in the left tail of the distribution, we adopt a “peak-over-threshold” method to derive the probability distribution of the left tail. For a given threshold u, the probability that the securities’ return will exceed the level u is defined as: Fu y Pr r u y r > u ;for y 0,r y u 1 - Fu Fu y F yu - F u If the threshold u is large enough, the distribution of the return exceeding u can be approximated by Generalized Pareto Distribution (GPD) with the following relationship. Fu y G, y The distribution of r can then be simplified as: F r 1F u G, y F u Therefore, F(u) can be estimated by (N-nu)/N where N is the number of observations with negative return and nu is the number of observations with return exceeding a threshold u. The cumulative density function of Generalized Pareto distribution, G,(y)is defined as: 1 y G, 1 - 1 + y -y 1 - e where 0 where 0 Where is a shape parameter and is a scale parameter. Then, the distribution of r can be revised as follow. N 1 - 1 + F r 1- u N - n y n y F r 1 - u 1 + N 1 N N - nu 1 Therefore, the VaR measure with the distribution based on extreme value theory method can be derived as: N VaR u + - 1 nu and can be estimated by a maximum likelihood method. Note that the probability density function of Generalized Pareto Distribution is represented by the following equation. f y 1 -1 y 1 1 where 0 As a result, the likelihood function can be shown as: 1 -1 1 y i L , y 1 - i=1 n Thus, the log likelihood is ln L , y - n ln + - 1 ln 1 i=1 n y i We can then solve the following equations for maximum likelihood estimators for and . 0 lnL , y 0 lnL , y and 2.3. Back-testing We test the result of a haircut valuation by BIS Basel back-testing. The BIS Basel backtesting method is used to test the accuracy of the model by testing the hypothesis whether the probability that the security price declines under haircut level more than %. That is, H0: Pb = H1: Pb > where Pb n,x : n 1 - x n-x x n = number of observations x = number of observations that the security price decline under haircut level = the probability that the security price declines under haircut (assigned to 0.01) There are three possible back-testing results; a. Green zone—if Pb 5%, the hypothesis cannot be rejected. Thus, the haircut result is acceptably accurate. b. Yellow zone—if 0.1% < Pb < 5%, the haircut result will be acceptable with BIS adjusted factor equal to Z Z where is equal to x/n. * c. Red zone—if Pb 0.1%, the haircut result is not acceptable. The new model or new method is required. 3. Haircut Results In this paper, we retrieve equity and bond daily price data from the Thai markets. For traded securities in the Stock Exchange of Thailand, daily prices of three groups of equity; SET50 index, non-SET50 Index, and warrants, are selected from the same window period; 6 February 2006 to 28 December 2008. There are 464 observations for each group of securities. For government bonds, five classes of daily bond price data, based on maturity1 (less then 1 year, 1 to 3 years, 3 to 7 years, 7 to 10 years, and more than 10 years), are taken from 4 January 2000 to 31 July 2008. We test the normality of securities return distribution with histogram and descriptive statistics for all acceptable collaterals. The VaR measures with both normality assumption and extreme value theory are then calculated along with BIS back-testing to confirm the accuracy of VaR measures for haircut results. 3.1. Normality Assumption To test a normality assumption on securities return, we plot the histogram of equity and bond returns, shown in figure 1 and 2, and calculate descriptive statistics. Most securities have excess kurtosis larger than zero. The tail distribution of both SET50 index and government bonds with all maturities appears to follow a normal distribution. However, returns of stocks in non-SET50 have much longer and heavier tail than suggested by a normal distribution. This implies that haircut valuation based on VaR with normality assumption may not be appropriate for stocks in non-SET50. 1 ThaiBMA bond maturity classification Figure 1: Histogram of Equity Returns a data Normal 0.12 tenday data Normal 20 18 16 0.1 14 Density Density 0.08 0.06 12 10 8 0.04 6 4 0.02 2 0 -10 -5 0 5 10 0 15 -0.1 -0.05 0 0.05 Data Data 0.1 0.15 (a) SET 50 0.2 (b) Non-SET50 Figure 2: Histogram of Government Bond Returns TB data Normal 500 TB data Normal 120 450 100 400 350 Density Density 80 300 250 60 200 40 150 100 20 50 0 -4 -3 -2 -1 0 1 2 3 4 0 5 Data -0.01 0 -3 x 10 0.01 Data (a) maturity < 1 year 60 0.03 0.04 (b) maturity 1-3 years TB data Normal 35 50 TB data Normal 30 25 Density 40 Density 0.02 30 20 15 20 10 10 5 0 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 Data 0.03 0.04 0.05 0.06 (c) maturity 3-7 years TB data Normal 25 Density 20 15 10 5 0 -0.1 -0.05 0 0.05 0.1 Data (e) maturity > 10 years 0.15 0 -0.04 -0.02 0 0.02 Data 0.04 0.06 0.08 (d) maturity 7-10 years 3.2. VaR With Normality Assumption Assume that common stocks’ returns are normally distributed with mean and standard deviation . The result of VaR with normality assumption for SET50 index and stocks in non-SET50 with 10-day horizon and 99% confidence level are shown in table 9. Note that the result of haircut rates for stocks in non-SET50 calculated by VaR with normality assumption may not be appropriate given the result of histogram and descriptive statistics in the previous section. Table 9 VaR with Normality Assumption for Common Stocks Average Standard Deviation VaR(99%) SET50 Non-SET50 2.37% 4.22% 12.20% 0.25% 5.03% 11.94% We classify warrants into three classes based on their liquidity—highly liquid, semiliquid, and illiquid warrants. Highly liquid, semi-liquid, and illiquid warrants are warrants that were traded more than 80% , from 60% to 80%, and less than 60% of the total number of trading days in data sample, respectively. From the total number of warrants of 71, there are only 3 warrants in semi-liquid class and 14 warrants in illiquid class. The haircut results based on 10-day 99% VaR with normality assumption are 50.73%, 55.06%, and 89.86% for highly liquid, semi-liquid, and illiquid warrants, respectively. It is important to note that the haircut results from a traditional VaR measure can mainly capture market risk. To take into account liquidity risk, the VaR measure was therefore adjusted upward by increasing horizon to 10 days. The results of VaR with normality assumption for government bond are shown in table 10. Table 10: VaR with Normality Assumption for Government Bond < 1 year Remaining Time to Matuarity 1 - 3 years 3 - 7 years 7 - 10 years > 10 years Mean 0.0280% 0.1298% 0.3565% -0.5105% -0.4999% Stdev VaR (99%) 0.2313% 0.5660% 0.5085% 1.3127% 1.5489% 3.9598% 2.5602% 5.4455% 3.1275% 6.7756% 3.3. VaR With Extreme Value Theory For different level of chosen threshold, u, we estimate shape and scale parameters of Generalized Pareto distribution by maximum likelihood method and calculate associated VaR measures shown in table 11. Table 11: VaR with Extreme Value Theory for Common Stocks in SET50 Index U 0.00% 4.57%*** (0.0044) 2.00% 4.42%*** (0.0052) 4.00% 4.72%*** (0.0066) 6.00% 3.06%*** (0.0055) 8.00% 3.00%*** (0.0073) 10.00% 1.17%** (0.005) -0.1714*** (0.0628) 182 182 -0.1952*** (0.0714) 113 182 -0.2695*** (0.0723) 65 182 -0.1308 (0.1086) 49 182 -0.1638 (0.1357) 24 182 0.2749 (0.3346) 13 182 nu N VaR (99% 14.55% 14.53% 14.83% 14.19% 14.31% ) * Significant at 90%, ** Significant at 95%, *** Significant at 99% 13.05% For common stocks in SET50 index, the values of shape parameter estimates, , are significantly less than zero, which implies that the tail of the distribution may be shorter than that of normal distribution. Therefore, VaR with normality assumption is more suitable for common stocks in SET50 index than VaR with extreme value theory. Table 12: VaR with Extreme Value Theory for Common Stocks in Non-SET50 U 0.00% 2.00% 4.00% 6.00% 2.99%*** 2.32%*** 2.38%*** 3.57% (0.0032) (0.004) (0.0063) (0.0214) 0.1649** 0.4029*** 0.5501** 0.5518 (0.0774) (0.1472) (0.2365) (0.5727) nu 175 95 49 24 N 175 175 175 175 VaR (99%) 20.62% 25.03% 26.73% 26.97% * Significant at 90%, ** Significant at 95%, *** Significant at 99% On the other hand, table 12 shows that the value of shape parameter estimates,, for common stocks in non-SET50, are all significantly greater than zero, which implies that the tail of the distribution is longer than that of normal distribution. These results confirm the findings from histogram and descriptive statistics that VaR with normality assumption may underestimate the actual loss. Therefore, VaR with extreme value theory is preferred for common stocks in non-SET50. Figure 3 shows that the tail distribution of stock returns in non-SET50 can be better explained by a GPD than by a normal distribution. Figure 3: Non-SET50 tail Distribution: GPD vs. Normal Distribution 4 tenday data Normal fit 12 3.5 3 Density 2.5 Generalized Pareto 2 1.5 Normal 1 0.5 0 0.06 0.08 0.1 0.12 0.14 Data 0.16 0.18 0.2 0.22 4. Haircut Rate and Back-testing 4.1. Haircut Rates The results of haircut rates are summarized in table 13 and 14. Given the results from a previous section, haircut rates for common stocks in SET50 and warrants are the ones based VaR measures with normality assumption whereas haircut rate for common stocks in non-SET50 is the one based on VaR measures with extreme value theory. For bonds, haircut rates are calculated based on VaR with normality assumption. Table 13: Haircut Rates for Equity Stock VaR (99%) with Normality Extreme Value Theory Warrant SET50 Non-SET50 Illiiquid Semi Liquid Highly Liquid 12.20% - 26.73% 89.86% - 55.06% - 50.73% - Table 14: Haircut Rates for Government Bond Remaining Time to Maturity < 1 Year 1- 3 Years 3 - 7 Years 7 - 10 Years > 10 Years 0.57% 1.31% 3.96% 5.45% 6.78% - - - - - VaR (99%) with Normality E xtreme Value Theory 4.2. Back-Testing Finally, we conduct a back-testing based on BIS Basel on all haircut rates. For equity back-testing, we use the data from 6 February 2006 to 28 December 2007 with the total number of 464 trading days. Given 464 observations, the BIS Basel back-testing result will fall into red, yellow, and green zones when the number of observations that the security price decline under haircut level are 8, 9 to 12, and 13 or more. 4.2.1. Common Stocks in SET50 Index and Non-SET50 Index There are only two days that the returns of stocks in SET50 index fall below the haircut level of 12.20%, shown figure 4. As a result, the haircut rate of 12.20% for stocks in SET50 index is in the green zone or is acceptably accurate based on BIS Basel backtesting. Figure 5 shows that the haircut rate for stocks in non-SET50 index also falls into a green zone of BIS Basel back-testing, where there is zero day that the return of stocks in non-SET50 index falls under the haircut rate of 26.73%. Figure 4: BIS Basel Back-testing for Stocks in SET50 Index Figure 5: BIS Basel Back-testing for Stocks in Non-SET50 (Haircut = 12.20% by VaR with Normality Assumption) (Haircut = 26.73% by VaR with Extreme Value Theory) 26.73% 24.40% 12.20% -24.40% 21 Dec 07 21 Oct 07 21 Nov 07 21 Sep 07 21 Jul 07 21 Aug 07 21 Jun 07 21 Apr 07 21 May 07 21 Mar 07 21 Jan 07 21 Feb 07 21 Dec 06 21 Oct 06 21 Nov 06 21 Sep 06 21 Jul 06 21 Aug 06 21 Jun 06 21 Apr 06 21 May 06 21 Mar 06 21 Feb 06 21 Dec 07 21 Oct 07 21 Nov 07 21 Sep 07 21 Aug 07 21 Jul 07 21 Jun 07 21 Apr 07 21 May 07 21 Mar 07 21 Jan 07 21 Feb 07 21 Dec 06 21 Oct 06 21 Nov 06 21 Sep 06 21 Jul 06 21 Aug 06 21 Jun 06 21 Apr 06 21 May 06 21 Mar 06 -12.20% 21 Feb 06 0.00% 0.00% -26.73% 4.2.2. Warrants Figure 6, 7, and 8 show that haircut rates for all three classes of warrants, highly liquid, semi-liquid, and illiquid, are acceptably accurate based on BIS Basel back-testing. There are only 4 out of 464 days that the return of highly liquid warrants fall under haircut rates of 50.73%. For semi-liquid and liquid warrants, there are 6 and 4 out of 464 days that the warrant lost its value more than haircut rates of 55.06% and 89.86%, respectively. Figure 6: BIS Basel Back-testing for Highly-liquid Warrant Figure 7: BIS Basel Back-testing for Semi-liquid Warrant (Haircut = 55.06% by VaR with Normality Assumption) (Haircut = 50.73% by VaR with Normality Assumption) 31.02% 34.66% 17.33% 15.51% 6 Dec 07 6 Nov 07 6 Oct 07 6 Sep 07 6 Aug 07 6 Jul 07 6 Jun 07 6 May 07 6 Apr 07 6 Mar 07 6 Feb 07 6 Jan 07 6 Oct 06 6 Dec 06 6 Nov 06 6 Sep 06 6 Jul 06 6 Aug 06 6 Jun 06 6 May 06 6 Apr 06 6 Mar 06 -17.33% 6 Feb 06 0.00% -51.99% -15.51% -69.32% -86.65% -31.02% Figure 8: BIS Basel Back-testing for Illiquid Warrant (Haircut = 89.86% by VaR with Normality Assumption) -112.04% -84.03% 56.02% 84.03% 112.04% 140.05% 70 ceD 6 70 voN 6 70 peS 6 70 t c O 6 70 guA 6 70 lu J 6 70 nu J 6 70 yaM 6 70 rpA 6 70 beF 6 70 na J 6 70 raM 6 60 ceD 6 60 voN 6 60 t c O 6 60 peS 6 60 guA 6 60 lu J 6 60 nu J 6 60 yaM 6 60 rpA 6 0.00% 28.01% 60 beF 6 -28.01% 60 raM 6 -56.02% 6 Dec 07 6 Oct 07 6 Nov 07 6 Sep 07 6 Aug 07 6 Jul 07 6 Jun 07 6 May 07 6 Apr 07 6 Mar 07 6 Jan 07 6 Feb 07 6 Dec 06 6 Nov 06 6 Oct 06 6 Sep 06 6 Aug 06 6 Jul 06 6 Jun 06 6 May 06 6 Apr 06 6 Mar 06 6 Feb 06 0.00% -34.66% 4.2.3. Government Bond The number of observations of government bond with each maturity class and their associated expected and actual number of exceptions, which are the number of observations that the government bond price declines by more than their haircut rates, under the BIS Basel back-testing framework are shown in table 15. Table 15: BIS Basel Backtesting for Government Bond Maturity (year) Number of Exceptions Number of observations Green Yellow Red <1 1-3 3-7 7-10 >10 1728 2341 2341 2341 2293 21 27 27 27 26 22-30 28-38 28-38 28-38 27-37 31 or more 39 or more 39 or more 39 or more 38 or more Actual Number of Exceptions 0 85 19 12 16 The actual number of exceptions indicates that BIS Basel back-testing results are in green, yellow, and red zone. In addition, figure 9 to 13 show the graphical BIS Basel back-testing results for each maturity class of government bonds. Figure 9: BIS Basel Back-testing for Government Bond (< 1 yr) (Haircut = 0.57% by VaR with Normality Assumption) 1.14% Figure 10: BIS Basel Back-testing for Government Bond (1- 3 yr) (Haircut = 1.31% by VaR with Normality Assumption) 5.2400% 3.9300% 0.57% 2.6200% 1.3100% Figure 11: BIS Basel Back-testing for Government Bond (3-7 yr) (Haircut = 3.96% by VaR with Normality Assumption) -7.9200% 7.9200% 18 Jan 08 18 Jan 07 18 Jan 06 18 Jan 05 18 Jan 04 18 Jan 03 18 Jan 02 18 Jan 01 (Haircut = 5.45% by VaR with Normality Assumption) -10.9000% 18 Jan 08 18 Jan 07 18 Jan 06 18 Jan 05 18 Jan 04 18 Jan 03 18 Jan 02 -5.4500% 18 Jan 01 0.0000% 18 Jan 00 80 na J 81 70 na J 81 60 na J 81 50 na J 81 40 na J 81 30 na J 81 20 na J 81 10 na J 81 00 na J 81 5.4500% 18 Jan 99 3.9600% Figure 12: BIS Basel Back-testing for Government Bond (7-10 yr) 10.9000% 99 na J 81 0.0000% 18 Jan 00 -2.6200% -0.57% -3.9600% -1.3100% 18 Jan 99 17 Jul 08 17 Mar 08 17 Jul 07 17 Nov 07 17 Mar 07 17 Jul 06 17 Nov 06 17 Mar 06 17 Jul 05 17 Nov 05 17 Mar 05 17 Jul 04 17 Mar 04 17 Nov 04 17 Jul 03 17 Nov 03 17 Mar 03 17 Jul 02 17 Nov 02 17 Mar 02 17 Jul 01 0.0000% 17 Nov 01 0.00% Figure 13: BIS Basel Back-testing for Government Bond (>10 yr) (Haircut = 6.78% by VaR with Normality Assumption) Figure 14: BIS Basel Back-testing for Government Bond (1- 3 yr) (Haircut = 2.61% by VaR with Extreme Value Theory) 80 na J 81 70 na J 81 60 na J 81 50 na J 81 40 na J 81 30 na J 81 20 na J 81 10 na J 81 0.0000% 6.7800% 00 na J 81 13.5600% 99 na J 81 -2.6100% 20.3400% 26 Mar 08 26 Mar 07 26 Mar 06 26 Mar 05 26 Mar 04 26 Mar 03 26 Mar 02 26 Mar 01 26 Mar 00 -6.7800% 26 Mar 99 0.0000% 2.6100% -13.5600% -20.3400% 5.2200% Except the class with 1 to 3 years to maturity that its back-testing result falls under the BIS Basel red zone, haircut rates for government bonds with all other maturity classes are acceptable accurate under the BIS Basel back-testing. The haircut rate of government bond with 1 to 3 years to maturity is thus recalculated by a new method, VaR with extreme value theory. Consequently, the haircut rate for this maturity class increases from 1.31% to 2.61%. We repeat BIS Basel back-testing process on this new haircut rate, shown in the figure 14, and find that it is in the BIS Basel green zone with 10 actual exceptions. 5. Benefits and Costs of Collateral The main benefit of collateral is credit risk reduction by liquidation value of collateral in the event of default even though the liquidation value may be less than its expected value. Collateral should also reduce the probability of default because the more collateral pledged, the larger loss amount experienced by the provider in the default event. As a result, higher haircut rates are preferable for clearing and settlement system. However, higher haircut rates increase the transaction costs for market participants and could have a negative effect on market growth. Although VaR with extreme value theory can provide a larger haircut rates than that derived by VaR with normality assumption, we propose that VaR with extreme value theory is used only when the tail distribution of securities’ return cannot be appropriately approximated by a normal distribution. We find that VaR with normality assumption is appropriate for common stocks in SET50 index, warrants, and government bonds with all maturities except for government bonds with maturity of 1 to 3 years, of which VaR with extreme value theory provides a better fit for haircut rate. For common stocks in non-SET50, VaR with extreme value theory can provide a more accurate haircut rate. Finally, to assure that the haircut rates derived from VaR with extreme value theory are not too large; we perform a risk-cost frontier analysis to confirm the optimal haircut solutions. Haircut rates and tail risk are compared at different levels of possible thresholds. The optimal haircut rate should be at the level that leads to an acceptable level of tail risk, but not too large for market participants. Figure 15 and 16 exhibit risk-cost frontier analysis for common stocks in non-SET50 and for government bond with maturity of 1 to 3 years. The results of risk-cost frontier confirm that, for all possible threshold levels, haircut rates by VaR with extreme value theory; 26.73% for common stocks in non-SET 50 and 2.61% for government bond with maturity of 1 to 3 years, are associated with the tail risk not over 1% or at 99% confidence level. Figure 15 Figure 16 Risk-Cost Frontier for Non-SET50 Risk-Cost Frontier for Bond with TTM 1-3 Years 0.11 0.1100 0.10 0.1000 0.09 0.0900 0.08 0.0800 EVT(2) EVT(4) 0.05 EVT(6) EVT(0.25) EVT(0.5) 0.0600 EVT(1.25) EVT(1.5) 0.0400 0.03 0.0300 0.02 0.0200 0.01 EVT(0.75) 0.0500 0.04 0.00 8.00% EVT(0) 0.0700 EVT(0) 0.06 Tail Risk Tail Risk 0.07 EVT(1.75) EVT(2.00) 0.0100 11.00% 14.00% 17.00% 20.00% 23.00% Haircut 26.00% 29.00% 32.00% 35.00% 38.00% 0.0000 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00% Haircut 6. Conclusion Collateral plays a very important role in mitigating credit risk in clearing and settlement system. Since there is a possible change in value of collateral from pledging and liquidating dates, haircut rate has been adopted in almost all exchanges to manage such additional market risk in potential default events. For most exchanges, a traditional approach for haircut valuation has been based on VaR with normality assumption. However, when the tail distribution of securities’ return cannot be fully explained by a normal distribution, the accuracy of haircut rates is in question. That is, when the securities’ return exhibits a longer and heavier tail than that of a normal distribution, haircut rates calculated by VaR with normality assumption will underestimate the true additional market risk in clearing and settlement system. An alternative approach to obtain a more accurate haircut rates is VaR with extreme value theory, where the tail of securities’ returns are assumed to follow Generalized Pareto Distribution (GPD) instead of a normal distribution. The optimal haircut rate should be the one that balances between the risk of clearing and settlement system and the transaction costs for market participants. We consider both equity and debt securities that are acceptable as collaterals. We use the Thai data to study a haircut valuation. Common stocks are split into two groups: common stocks in SET50 index and stocks in non-SET50 index. Warrants are classified into three classes according their liquidity; highly liquid, semi-liquid, and illiquid. Government bonds are categorized into five classes based on their maturity. Haircut rates for each type of collateral are calculated with two main approaches: VaR with normality assumption and VaR with extreme value theory based on GPD. We conduct BIS Basel back-testing on all haircut rates and find that VaR with normality assumption is appropriate for a haircut valuation of common stocks in SET50 index, warrants, and government bonds with maturity of less than 1 year, 3 to 7 years, 7 to 10 years, and longer than 10 years, while VaR with extreme value theory is appropriate for a haircut valuation for stocks in non-SET50 index and government bonds with maturity of 1 to 3 years. We conduct a risk-cost frontier analysis for haircuts calculated by VaR with extreme value theory. 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